Britain's third-largest bank yesterday announced formally a proposed takeover of the 14th-largest American bank firm, Crocker National Corp., and the news prompted swift reaction on Capitol Hill.

Midland Bank Ltd. of London confirmed reports that circulated Monday night of its plans to buy a controlling interest in Crocker, a San Francisco holding company for Crocker National Bank.

Within hours, Rep. Fernand St. Germain (D-R.I.), chairman of the House financial institutions subcommittee, scheduled three days of hearing after Labor Day to "explore fully how these acquisitions are impacting on domestic banks, the U.S. regulatory structure and the American Consumer."

The $820 million Midland-Crocker deal, which is subject to approval by Crocker stockholders and U.S. banking regulators, would be the largest foreign bank takeover in American history. At the same time, Midland agreed in principle yesterday to assume a 60 percent interest in a German bank, Trinkaus & Burkhardt, that is now held by Citi-corp.

Rep. Benjamin Rosenthal (D.-N.Y.), who held hearing last month on the acquisition of the Marine Midland Banks in New York State by the Hong-kong and Shanghai Banking Corp., expressed "deep concern" yesterday over the newest takeover respect.

He called it "unwise and even irresponsible" of the Federal Reserve and the Comptroller of the Currency to "rush pell-mell to encourage foreign takeovers of U.S. banks at a time when the public and the Congress have expressed growing alarm over rapidly increasing foreign ownership of U.S. firms."

Last week, Fed Chairman Paul Volcker told the Senate Banking Committee he saw no need to reinstitute a congressional moratorium on foreign takeovers of U.S. banks because there was "no evidence at this point that foreign ownership in itself has led, or is likely to led, to bank supervisory problems. Nor have the banks involved, or the communities they serve, been harmed." The American Bankers Association supports this view.

However, a forthcoming report by the General Accounting Office, Congress' watchdog agency, reportedly will urge that a moratorium of indefiinite duration to be reimposed. The GAO is concerned that U.S. banking laws offer foreign banks a competitive advantage over American banks because domestic institutions effectively are banned from making similar takeover bids.

Independent presidential candidate John Anderson, in a paper released yesterday, declared, "As a matter of policy we ought not to give foreign banks an unfair competitive advantage. For that reason, some means of assuring parity is absolutely imperative."

The Carter administration is preparing to release a long-awaited study advocating liberalization of banking laws to permit bank holding companies to acquire banks in other states. Current laws, it contends, have become archaic in a time of technological changes -- meaning effective branching by electronics and competition from nonbank institutions, such as brokerage houses and even retail stores.

Both reasons were cited by Crocker and Midland in a joint statement, which said: "The world of finance is undergoing changes more dramatic than any in modern history . . . . National boundaries that formerly segregated markets are fast eroding."

During the 1970s, according to a Federal Reserve study, foreign interest in ownership of U.S. banks increased dramatically. The number of banks owned by foreigners grew from about 30 im 1972 to three times that many in 1979. Since 1974 there have been nine U.S. bank acquisitions by foreign banks with assets of more than $500 million.

A Midland-Crocker deal would make California the leading U.S. center for foreign banks -- with 29 foreign-owned institutions and assets of $37 billion -- followed by New York State with 26 foreign-owned banks and assets of $29 billion.

Under the agreement with Crocker, Midland would acquire 51 percent of Crocker's stock by buying $495 million in new common stock from Crocker, or 3 1/2 million shares at $90, and purchasing another 6 1/2 million in existing shares at book value, or the per-share value of Crocker's assets minus its liabilities.

Midland will pay no more than $50 a share for the 6 1/2 million existing common shares. Stock in the San Francisco-based bank has traded recently for about $36 a share.

The bank sale could take as long as 15 months to complete, a Crocker spokesman said. If it is agreed to as proposed, Midland would own more than 66 percent of Crocker, or 12 million of Crocker's 18 million shares outstanding.

Crocker has assets totaling $16.9 billion and 370 branches in California. Midland is the parent company of the Midland Bank Group, which has 3,500 branches in the United Kingdom and Ireland.

Malcolm Wilcox, chief general manager of Midland, called Midland's agreement a "partnership" with Crocker, a bank which Wilcox said has deep roots in the American market.

Crocker Chairman Thomas Wilcox, no relation to Midland's Wilcox, said the most important advantage of the agreement to Crocker is the infusion of nearly half a billion dollars in capital.

Last year Crocker reported $117 million in profits, up nearly 56 percent over 1978 when the bank reported a $75.2 million net.